trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

A simple-spectrum Gibbs-stochastic matrix for every positive vector

Every strictly positive Gibbs vector admits a column-stochastic matrix with simple complex spectrum.

Closed Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH8
DOCUMENT LINKS0
THEOREM

A reversible chain with simple spectrum

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Constrained harmonic optimizationConstrained harmonicoptimizationZeitlin Six-J InverseZeitlin Six-J InverseA self-dual factorization of an irreducible thermal processA self-dual factorization of anirreducible thermal processA simple-spectrum Gibbs-stochastic matrix for every positive vectorA simple-spectrum Gibbs-stochastic matrix for everypositive vectorEven looped paths allow the non-symmetric Strong Spectral PropertyEven looped paths allow thenon-symmetric Strong SpectralProperty
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Lean sourceResearch workspace
Status
Closed
Depth
8
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Matrix/GibbsStochasticSimpleSpectrum
Repository path
D5/S3/Quantum/Matrix/GibbsStochasticSimpleSpectrum.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.